考虑粗糙表面的复杂产品装配精度预测研究

doi:10.11996/JG.j.2095-302X.2026010162

图学学报 ›› 2026, Vol. 47 ›› Issue (1): 162-172.DOI: 10.11996/JG.j.2095-302X.2026010162

考虑粗糙表面的复杂产品装配精度预测研究

王刚锋¹(), 张寰¹, 杨英英², 刘一涛³, 郭彦云³, 岳萍⁴, 孙岩辉¹

¹ 长安大学道路施工技术与装备教育部重点实验室，陕西西安 710064
² 西安财经大学行知学院，陕西西安 710038
³ 中铁宝桥集团有限公司，陕西宝鸡 721006
⁴ 国营四达机械制造公司，陕西咸阳 712200

收稿日期:2025-06-05 接受日期:2025-10-10 出版日期:2026-02-28 发布日期:2026-03-16
通讯作者:王刚锋，E-mail：wanggf@chd.edu.cn
基金资助:
陕西省“十四五”教育科学规划课题(SGH22Y1274);陕西省自然科学基金实验室重点项目(2025SYS-SYSZD-104);教育部产学合作协同育人项目(230802436213147);山东省土方机械智慧施工技术重点实验室资助项目(PKL2024F13)

Research on assembly accuracy prediction of complex products considering rough surfaces

WANG Gangfeng¹(), ZHANG Huan¹, YANG Yingying², LIU Yitao³, GUO Yanyun³, YUE Ping⁴, SUN Yanhui¹

¹ Key Laboratory of Road Construction Technology and Equipment of MOE, Chang’an University, Xi’an Shaanxi 710064, China
² Xingzhi College, Xi’an University of Finance and Economics, Xi’an Shaanxi, 710038, China
³ China Railway Baoji Bridge Group Co., Ltd., Baoji Shaanxi 721006, China
⁴ State Sida Machinery Manufacturing Company, Xianyang Shaanxi 712200, China

Received:2025-06-05 Accepted:2025-10-10 Published:2026-02-28 Online:2026-03-16
Supported by:
Educational Scientific Planning Project of the 14th Five-Year Plan of Shaanxi Province(SGH22Y1274);Laboratory Key Project of Natural Science Foundation of Shaanxi Province(2025SYS-SYSZD-104);Collaborative Education Project of Industry-University Cooperation of the Ministry of Education(230802436213147);Project of Key Laboratory of Earthmoving Machinery Intelligent Construction Technology of Shandong Province(PKL2024F13)

摘要/Abstract

摘要：

针对现有复杂产品装配精度预测中未充分考虑粗糙表面对装配精度的影响，导致精度预测不准确及实际装配适用性不足的问题，提出一种考虑粗糙表面的装配精度预测方法。首先，构建装配精度信息模型，表达零件配合特征、几何公差及粗糙度信息，并以此为基础，构建装配精度知识图谱；其次，基于小位移旋量(SDT)理论建立几何公差表示模型，并研究平面零件及柱面零件粗糙表面模拟方法及小位移旋量表达式确定方法；再次，根据装配序列确定装配体偏差传递路径，并构建装配接触有向图，利用雅可比-粗糙表面模型实现装配精度预测。最后，以某型号工程机械曲柄连杆机构为例验证方法可行性，结果表明，该方法可实现装配精度的准确预测并对实际装配具有指导价值。

关键词: 装配精度预测, 粗糙表面, 知识图谱, 小位移旋量, 雅可比矩阵

Abstract:

Given that the impact of rough surfaces on assembly accuracy had been insufficiently considered in the existing assembly accuracy prediction for complex products, leading to inaccurate precision prediction and limited practical assembly applicability, an assembly-accuracy prediction method considering rough surfaces was proposed. Firstly, an assembly-accuracy information model was constructed to express mating feature, geometric tolerance, and roughness information. Based on the model, an assembly-precision knowledge graph was constructed. Secondly, a geometric-tolerance representation model was established based on the Small-Displacement Torsor (SDT) theory; a simulation method for rough surfaces of plane and cylindrical parts as well as a determination method of SDT expressions were studied. Thirdly, the error-propagation path of the assembly was determined according to the assembly sequence, and a pose-relationship graph for the assembly was constructed. Then, the assembly-precision prediction was achieved using a Jacobian-torsor model. Finally, the feasibility of the method was verified using the crank-connecting-rod mechanism of a specific construction-machine model as an example. The simulation results demonstrated that the method could achieve accurate assembly-precision prediction and provided valuable guidance for practical assembly operations.

Key words: assembly accuracy prediction, rough surface, knowledge graph, small displacement torsor, Jacobian matrix

中图分类号:

TG95

王刚锋, 张寰, 杨英英, 刘一涛, 郭彦云, 岳萍, 孙岩辉. 考虑粗糙表面的复杂产品装配精度预测研究[J]. 图学学报, 2026, 47(1): 162-172.

WANG Gangfeng, ZHANG Huan, YANG Yingying, LIU Yitao, GUO Yanyun, YUE Ping, SUN Yanhui. Research on assembly accuracy prediction of complex products considering rough surfaces[J]. Journal of Graphics, 2026, 47(1): 162-172.

图/表 19

参考文献 18

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公差带	SDT表达式	变量变动范围
圆度	$D={[\begin{array}{cccccc}{d}_{x}& {d}_{y}& 0& 0& 0& 0\end{array}]}^{\text{T}}$	$\begin{array}{l}-\frac{{T}_{c}}{2}\le {d}_{x}\le \frac{{T}_{c}}{2}\\ -\frac{{T}_{c}}{2}\le {d}_{y}\le \frac{{T}_{c}}{2}\end{array}$
平面度	$D={[\begin{array}{cccccc}0& 0& {d}_{z}& {\theta }_{x}& {\theta }_{y}& 0\end{array}]}^{\text{T}}$	$\begin{array}{cc}-\frac{{T}_{f}}{2}\le {d}_{z}\le \frac{{T}_{f}}{2}& \begin{array}{c}-\frac{{T}_{f}}{b}\le {\theta }_{x}\le \frac{{T}_{f}}{b}\\ -\frac{{T}_{f}}{a}\le {\theta }_{y}\le \frac{{T}_{f}}{a}\end{array}\end{array}$
圆柱度	$D={[\begin{array}{cccccc}0& {d}_{y}& {d}_{z}& 0& {\theta }_{y}& \theta \end{array}]}^{\text{T}}$	$\begin{array}{cc}-\frac{{T}_{c}}{2}\le {d}_{y}\le \frac{{T}_{c}}{2}& -\frac{{T}_{c}}{l}\le {\theta }_{y}\le \frac{{T}_{c}}{l}\\ -\frac{{T}_{c}}{2}\le {d}_{z}\le \frac{{T}_{c}}{2}& -\frac{{T}_{c}}{l}\le {\theta }_{z}\le \frac{{T}_{c}}{l}\end{array}$
直线度	$D={[\begin{array}{cccccc}0& {d}_{y}& {d}_{z}& 0& {\theta }_{y}& \theta \end{array}]}^{\text{T}}$	$\begin{array}{cc}-\frac{{T}_{c}}{2}\le {d}_{x}\le \frac{{T}_{c}}{2}& -\frac{{T}_{c}}{l}\le {\theta }_{x}\le \frac{{T}_{c}}{l}\\ -\frac{{T}_{c}}{2}\le {d}_{y}\le \frac{{T}_{c}}{2}& -\frac{{T}_{c}}{l}\le {\theta }_{y}\le \frac{{T}_{c}}{l}\end{array}$
平行度	$D={[\begin{array}{cccccc}0& 0& {d}_{z}& {\theta }_{x}& {\theta }_{y}& 0\end{array}]}^{\text{T}}$	$\begin{array}{cc}-\frac{{T}_{p}}{2}\le {d}_{z}\le \frac{{T}_{p}}{2}& \begin{array}{c}-\frac{{T}_{p}}{b}\le {\theta }_{x}\le \frac{{T}_{p}}{b}\\ -\frac{{T}_{p}}{a}\le {\theta }_{y}\le \frac{{T}_{p}}{a}\end{array}\end{array}$

公差带	SDT表达式	变量变动范围
圆度	$D={[\begin{array}{cccccc}{d}_{x}& {d}_{y}& 0& 0& 0& 0\end{array}]}^{\text{T}}$	$\begin{array}{l}-\frac{{T}_{c}}{2}\le {d}_{x}\le \frac{{T}_{c}}{2}\\ -\frac{{T}_{c}}{2}\le {d}_{y}\le \frac{{T}_{c}}{2}\end{array}$
平面度	$D={[\begin{array}{cccccc}0& 0& {d}_{z}& {\theta }_{x}& {\theta }_{y}& 0\end{array}]}^{\text{T}}$	$\begin{array}{cc}-\frac{{T}_{f}}{2}\le {d}_{z}\le \frac{{T}_{f}}{2}& \begin{array}{c}-\frac{{T}_{f}}{b}\le {\theta }_{x}\le \frac{{T}_{f}}{b}\\ -\frac{{T}_{f}}{a}\le {\theta }_{y}\le \frac{{T}_{f}}{a}\end{array}\end{array}$
圆柱度	$D={[\begin{array}{cccccc}0& {d}_{y}& {d}_{z}& 0& {\theta }_{y}& \theta \end{array}]}^{\text{T}}$	$\begin{array}{cc}-\frac{{T}_{c}}{2}\le {d}_{y}\le \frac{{T}_{c}}{2}& -\frac{{T}_{c}}{l}\le {\theta }_{y}\le \frac{{T}_{c}}{l}\\ -\frac{{T}_{c}}{2}\le {d}_{z}\le \frac{{T}_{c}}{2}& -\frac{{T}_{c}}{l}\le {\theta }_{z}\le \frac{{T}_{c}}{l}\end{array}$
直线度	$D={[\begin{array}{cccccc}0& {d}_{y}& {d}_{z}& 0& {\theta }_{y}& \theta \end{array}]}^{\text{T}}$	$\begin{array}{cc}-\frac{{T}_{c}}{2}\le {d}_{x}\le \frac{{T}_{c}}{2}& -\frac{{T}_{c}}{l}\le {\theta }_{x}\le \frac{{T}_{c}}{l}\\ -\frac{{T}_{c}}{2}\le {d}_{y}\le \frac{{T}_{c}}{2}& -\frac{{T}_{c}}{l}\le {\theta }_{y}\le \frac{{T}_{c}}{l}\end{array}$
平行度	$D={[\begin{array}{cccccc}0& 0& {d}_{z}& {\theta }_{x}& {\theta }_{y}& 0\end{array}]}^{\text{T}}$	$\begin{array}{cc}-\frac{{T}_{p}}{2}\le {d}_{z}\le \frac{{T}_{p}}{2}& \begin{array}{c}-\frac{{T}_{p}}{b}\le {\theta }_{x}\le \frac{{T}_{p}}{b}\\ -\frac{{T}_{p}}{a}\le {\theta }_{y}\le \frac{{T}_{p}}{a}\end{array}\end{array}$

雅可比矩阵	矩阵值	雅可比矩阵	矩阵值
${J}_{s1P1}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& -151& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 151& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$	${J}_{s2P3}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& -151& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 151& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$
${J}_{s2P1}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& -151& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 151& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$	${J}_{s3P3}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& -151& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 151& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$
${J}_{s1P2}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& -151& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 151& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$	${J}_{s1P4}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& 15& 0\\ 0& 1& 0& -15& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$
${J}_{s1P3}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& -151& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 151& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$	${J}_{s1P5}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$

雅可比矩阵	矩阵值	雅可比矩阵	矩阵值
${J}_{s1P1}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& -151& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 151& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$	${J}_{s2P3}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& -151& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 151& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$
${J}_{s2P1}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& -151& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 151& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$	${J}_{s3P3}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& -151& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 151& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$
${J}_{s1P2}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& -151& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 151& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$	${J}_{s1P4}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& 15& 0\\ 0& 1& 0& -15& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$
${J}_{s1P3}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& -151& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 151& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$	${J}_{s1P5}$	$\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]$

接触面配合	配合类型	SDT表达式
s1P1-s1P2	柱面配合	${[\begin{array}{cccccc}-0.1157& -0.2483& 0& -0.0461& -0.0232& 0\end{array}]}^{\text{T}}\times {10}^{-2}$
s2P1-s1P3	平面配合	${[\begin{array}{cccccc}0& 0& 0.1302& 0.0316& -0.1455& 0\end{array}]}^{\text{T}}\times {10}^{-2}$
s2P3-s1P2	柱面配合	${[\begin{array}{cccccc}-0.1206& -0.2357& 0& -0.0391& -0.0209& 0\end{array}]}^{\text{T}}\times {10}^{-2}$
s3P3-s1P4	柱面配合	${[\begin{array}{cccccc}-0.156& -0.2195& 0& -0.0396& -0.0301& 0\end{array}]}^{\text{T}}\times {10}^{-2}$
s1P4-s1P5	柱面配合	${[\begin{array}{cccccc}-1.498& -0.653& 0& -0.0511& -0.0326& 0\end{array}]}^{\text{T}}\times {10}^{-3}$

考虑粗糙表面的复杂产品装配精度预测研究

Research on assembly accuracy prediction of complex products considering rough surfaces

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